ed1410 mathematics for enrichment

8/2/2019 ED1410 Mathematics for Enrichment

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ED1410 Mathematics ForEnrichment

Tessellations

Name:Dk Hjh Fatin Farhana Pg Hj Metassan

Reg No: 09B4065

Faculty Of Business , Economics & Policy Studies


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What is Tessellation?

Tessellation is created when a shape is

repeated over and over again covering a plane

without any gaps or overlaps.

word "tessellation" comes from the Latin word

tessella the tessera, or small square tile

used in producing mosaics.

word "tessellate" is derived from the Ionic

version of the Greek word "tesseres," which in

English means "four."
http://www.artlex.com/ArtLex/T.htmlhttp://www.artlex.com/ArtLex/m/mosaic.htmlhttp://www.artlex.com/ArtLex/m/mosaic.htmlhttp://www.artlex.com/ArtLex/T.html


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History Of

Tessellations

Maurits Cornelius Escher

- In 1936, Escher embarked on an important

journey to the Alhambra in Granada, Spain.

The Moorish tilings he saw there fascinated

him

- he created a number of fascinating

landscapes, portraits, and geometric

designs, but the work for which he is most

famous, his tessellations

- animated his own versions of the abstract

geometrical designs


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Rule Of Tessellation

- Rule #1: the tessellation must tile a floor with

no overlapping or gaps.

- Rule #2: The tiles must be regular and all the

same

- Rule #3: Each vertex must look the same


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Types Of Tessellations

Regular Tessellations

- a tessellation or tiling using only one type of

regular polygon

Interior angle of each square:

90 degrees

90 + 90 + 90 +90 = 360 degrees

Interior of each equilateral

triangle: 60 degrees

60 + 60 + 60 + 60 + 60 + 60 =

360 degrees


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Regular Tessellations

Interior angle of each

pentagon : 108 degrees

108 + 108 + 108 =324

degrees

Cant tessellate!

WHY? It overlaps!

all polygons with more than six sides will overlap! So, the only regular

polygons that tessellate are triangles, squares and hexagons!


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Vertex

Is just a corner point

3 hexagons meet at the

vertex and a hexagon

has 6 sides So, it is known as

6.6.6 tessellation

For a regulartessellation,the pattern

is identical at each

vertex.


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Semi-regular Tessellations

- tessellation or tiling using two or more types of

regular polygons

3.3.3.3.6

60+60+60+60+120 =

360 degrees

3.6.3.6

60+120+60+120=

360 degrees


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Semi-regular Tessellations

To name a tessellation, simply work your way around

one vertex counting the number of sides of the

polygons that form that vertex

Always start at the polygon with the least number ofsides, so 3.12.12 NOT 12.3.12


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Vertex Configuration

a series of numbers which represent the arrangement of

polygons surrounding any random vertex of a regular or semi-

regular tessellation

What does 3.4.6? It refers to an equilateral triangle, square

and regular hexagon surrounding any random vertex point in

the tessellation

A {3, 4, 6} vertex configuration will not work because the sum

of the interior angle measures of an equilateral triangle,

square, and hexagon will sum to

60 + 90 + 120 = 270, but for a configuration to tessellate, the

sum must be 360.


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Demi-regular Tessellation

- curved shapes (not just polygons)

Eagles Curvy shapes


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Symmetry In Tessellations

Translational Symmetry

- every point of the pre-

image is moved the

same distance in thesame direction to form

the image

- without rotation or

change in size.


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Rotational Symmetry

- performed by "spinning"

the object around a fixed

point known as the center

of rotation.

- can rotate your object at

any degree measure, but

90 and 180 are two of the

most common. Also,rotations are done

counterclockwise!


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Glide Reflectional

Symmetry

- a "flip" of an object over

a line a combination of a

reflection and a

translation. Whether

the reflection happens

first or second does not

matter


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Tessellations in Everyday Life

Scale of a

fish

Scale of a

snake

Beehive

Bricks

pavement

Tiles


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References

http://mathforum.org/sum95/suzanne/historytess.html

http://www.coolmath.com/lesson-tessellations-1.htm

http://mathworld.wolfram.com/Tessellation.html

http://www.sdmf.k12.wi.us/mfhs/tessellation/index.htm

http://mathworld.wolfram.com/SemiregularTessellation.html

http://nrich.maths.org/4832

http://library.thinkquest.org/16661/simple.of.regular.polygons/semiregular.2.html

http://library.thinkquest.org/16661/simple.of.regular.polygons/semiregular.1.html

#Anchor-Introduction-65209

http://members.cox.net/tessellations/Symmetry.html

http://www.beva.org/math323/asgn5/tess/regpoly.htm

http://www.coolmath4kids.com/tesspag1.html

http://www.ehow.com/about_5078949_definitions-translation-tessellation.html

http://illuminations.nctm.org/Lessons/Tessellations/Tessellations-AK.pdf

http://library.thinkquest.org/16661/escher.html

http://www.gradeamathhelp.com/transformation-geometry.html

http://library.thinkquest.org/16661/background/symmetry.4.html
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